Let's simplify each part step by step.
1. Simplify 64f^0:
Remember that any number or letter raised to the power of 0 is 1 (except when the base is zero). So:
f^0 = 1
Therefore:
64f^0 = 64 × 1 = 64
2. Simplify (16x^8)^{3/4}:
This means raising 16x^8 to the power 3/4. Let's break it into steps:
- Write inside the parenthesis separately: 16 and
x^8. - Apply the power to both:
16^{3/4}and(x^8)^{3/4}. - Simplify
16^{3/4}: - First find the 4th root of 16 because of the denominator 4. The 4th root of 16 is 2 (since 2^4 = 16). - Now raise that result to the power 3:2^3 = 8. - Simplify
(x^8)^{3/4}: - When raising a power to a power, multiply the exponents:8 × (3/4) = 24/4 = 6. - So,(x^8)^{3/4} = x^6.
Putting it together:
(16x^8)^{3/4} = 8x^6
Final answers:
64f^0 = 64(16x^8)^{3/4} = 8x^6